Consider the circle of radius 5 centered at (0,0). find an equation of the line tangent to the circle at point (3,4). the book gives me the y=-3/4(x-3) but can you explain to me how you get this answer?

Equation of the circle: x² + y² = 25
9 + 16 = 25 => the point (3,5) is on the circle.
the line tangent to the circle is perpendicular to the radius O point
slope of the radius: 4/3 => slope of the tangent = -3/4
tangent contain (3,4) and have -3/4 as slope.
so equation is : y - 4 = -3/4 (x - 3) => y = -3/4x - 4 + 9/4 + 4 => y = -3/4x + 9/4 
or y = -3/4(x-3)